Reference to tomographic measurements of electrical conductivity distribution in a sample are intended to mean that the conductivity distribution of a sample, which can be a ground sample, aquifer sample, other geological sample, but also biological materials and the like in turn of the various cross sections through the sample.
For understanding of practically all significant questions in conjunction with heterogeneously structured samples, a knowledge of the spatial structure of the sample is of paramount significance. In the case of a heterogeneously structured sample, for example ground, aquifers and other geological samples, this knowledge has required above all invasive processes, for example, test drilling. Such invasive processes have the drawback that they alter the conditions in the sample. Furthermore, the determination of the structure only takes place at selected points in the sample. Important relationships can remain undiscovered and this applies in particular to transport processes in subterranean strata.
More recently, less intensive geophysical and geoelectrical methods have been developed for geological investigations. It is possible, for example, to measure a variety of geological parameters by noninvasive methods or methods which are less invasive, utilizing sensors which can be forced into the ground or are provided in the region of the ground and which measure geological parameters directly or measure parameters which can be interpreted in turn by biological structures.
For example, a geoelectric method is known whereby at least two electrodes are inserted into the ground and a voltage measuring unit is connected with the electrodes so that the electrical potential distribution can be measured and from that distribution the electrical conductivity distribution can be determined.
Another method known to the art, namely, controlled source audiomagnetotelluric (CSAMT) provides one or more electrical dipoles in the ground which are driven in the frequency range of 1 Hz to 8 kHz at a relatively large distance from such a dipole (often several kilometers) a magnetic and electrical component of the radiated electromagnetic waves are measured. With this process geological structures can be determined at a considerable depth and distance.
A geoelectromagnetic method is likewise known whereby the ground is excited with coils on the ground surface or by means of a transmitter spaced therefrom and a magnetic field induced subterraneously by reaction with external magnetic field is measured.
From DE 198 37 828, a method of calculating a current density distribution in a subterranean sample is known in which two electrodes are implanted in the ground sample. A low-frequency electrical alternating current is supplied to the electrode and a current density distribution of this current is effected in the subterranean sample as a function of the conductivity distribution therein. This results in a magnetic field intensity distribution which can be measured with the aid of a magnetic field sensor. From the magnetic field distribution the current density distribution can be calculated. This in turn allows the conductivity distribution in the subterranean sample to be determined. The conductivity of the sample is the target value and allows properties of the sample to be determined. DE 198 37 828 also discloses an apparatus for carrying out that method using a lock-in amplifier evaluating the measured signal.
As a general matter, in conductometry the measurement of the voltage drop or the potential difference in a sample to be investigated is a prerequisite for calculating the conductivity of the sample. For this purpose, the sample can be supplied for example with alternating current. From the measured potential differences and the amplitude of the current measured in the conductors supplying that alternating current, the specific electrical resistance and its converse, the conductivity of the sample, can be calculated. In cases in which the magnetic field strength distribution is to be measured, the conductivity of the sample can be calculated as well from the measured current amplitude and the magnetic field strength.
In geoelectric measurements the multidimensional conductivity distribution in samples can be determined for example by the application of current and the measurement of potential differences. For this purpose, the sample is usually contacted with a large number of electrodes. An alternating current is preferably launched into the sample by each two electrodes of this array of electrodes, for example into the ground. Each application of alternating current generates an associated electric potential distribution as a function of the electrical conductivity distribution in the sample. At other electrodes the potential difference is measured.
From the measured electrical potential and/or the measured magnetic field for a sufficiently large number of different applications of electrical excitation signals, the conductivity distribution in the sample can be calculated by means of special calculating techniques. The method of application of current and measurement of electrical or magnetic fields is used in many geophysical investigations with different electrode arrangements, like, for example, the Schlumberger sounding, Wenner mapping, dipole-dipole arrangements, four-point measurements in two-dimensional or three-dimensional tomography (electrical resistivity tomography: ERT) with flat or round electrode elements.
A drawback of earlier measurement systems and methods is that the current supply requires energization of respective pairs of electrodes of the entire set. The total measurement time thus corresponds to the sum of the individual measurements for an excitation. The total measurement time is a function of the measurement arrangement and the desired resolution and precision and thus can be very long. When for example an individual measurement for a particular precision requires a measurement time of 30 minutes, the total measurement time for 10 excitations can consume 5 hours. In samples in which the conductivity distribution is the targeted parameter and the measurement should be carried out in a shorter period of time, the measurement devices of the prior art have not been found to be suitable.
In Cheney et al (Cheney, M., Isaacson, D., Newell, J. D., 1999. Electrical impedance tomography. SIAM Review, Vol. 41. pp 85-101) a method of electrical impedance tomography has been described in which the electrical conductivity measurement of a human body utilizes the application of electric currents independently from one another and in succession. A drawback of this system is that the measurement device is only suitable for samples like those of the human body. More complex samples, for example, geophysical samples, cannot be characterized by such systems or are characterizable only limitedly by them.